This question is about code but seeing as I've been looking at HAC estimates recently in R I will "answer".
I have not checked the R implementation of Newey-West is exactly as in their original paper. However, your code does indeed calculate R's NeweyWest HAC estimate using the default bandwidth selection/lag method. (You can view this parameter with the "verbose=T" option.)
If you know the form of the correlations in your data then you can take less of a "sledgehammer" approach than Newey-West. E.g. Prais-Winsten or Cochrane-Orcutt.
Be aware that serial correlation is being examined here and so the order that your observations are sorted in does matter.
If you are interested you might consider a toy example where you generate correlated residuals on purpose to see how the Newey-West std error estimates/p-values differ. In the example below the correlated residuals make it "look like" the response can be fitted against a straight line. The lag parameter is automatically (and correctly) chosen = 1 (seen with verbose=T option). If you play with the process generating the residuals you can see how it changes.
correlated_residuals<-arima.sim(list(ar = .9), n)
summary(fit) # standard estimates